Title: Shrinkage priors for circulant correlation structure models Show Chinese title

Title: 收缩先验用于循环相关结构模型

Abstract: We consider a new statistical model called the circulant correlation structure model, which is a multivariate Gaussian model with unknown covariance matrix and has a scale-invariance property. We construct shrinkage priors for the circulant correlation structure models and show that Bayesian predictive densities based on those priors asymptotically dominate Bayesian predictive densities based on Jeffreys priors under the Kullback-Leibler (KL) risk function. While shrinkage of eigenvalues of covariance matrices of Gaussian models has been successful, the proposed priors shrink a non-eigenvalue part of covariance matrices. Show Chinese abstract

Abstract: 我们考虑了一种新的统计模型，称为循环相关结构模型，这是一种具有未知协方差矩阵的多元高斯模型，并且具有尺度不变性。 我们为循环相关结构模型构建了收缩先验，并证明基于这些先验的贝叶斯预测密度在Kullback-Leibler（KL）风险函数下渐近地优于基于Jeffreys先验的贝叶斯预测密度。 虽然高斯模型的协方差矩阵的特征值收缩已经取得了成功，但所提出的先验收缩了协方差矩阵的非特征值部分。